Monogenic function

A monogenic function is a complex function with a single finite derivative.
More precisely, a function defined on is called monogenic at, if exists and is finite, with:
Alternatively, it can be defined as the above limit having the same value for all paths. Functions can either have a single derivative or infinitely many derivatives, with no intermediate cases. Furthermore, a function which is monogenic, is said to be monogenic on, and if is a domain of, then it is analytic as well
The term monogenic was coined by Cauchy.